Oscillations of a spring: (force of spring), , vertical spring equilibrium: ; A = max speed, 2a = max acceleration | ; (f = frequency, t = period) (k is spring constant) = (vmax at equilibrium x=xo) = angular frequency, = phase shift. Critically damped, reaches equilibrium in the shortest time: , underdamped, several swings/oscillations before reaching equilibrium/rest: , overdamped ,takes a long time to reach equilibrium but no oscillating: A spring/mass system will have its own natural frequency , but an external force can cause a forced oscillation on the system. Equation (prob not needed): where and. Q value: quality factor , specifies the height and narrowness of a resonant peak. (where is the difference between the two frequencies at which the resultant amplitude is of the max amplitude) Longitudinal wave: (solid) or (fluid) ( is elastic modulus, b is bulk modulus, is density)